Deterministic Parameterized Connected Vertex Cover

  • Marek Cygan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)

Abstract

In the Connected Vertex Cover problem we are given an undirected graph G together with an integer k and we are to find a subset of vertices X of size at most k, such that X contains at least one end-point of each edge and such that X induces a connected subgraph. For this problem we present a deterministic algorithm running in O(2kpoly(n)) time and polynomial space, improving over the previous-best O(2.4882kpoly(n)) time deterministic algorithm and O(2kpoly(n)) time randomized algorithm. Furthermore, when usage of exponential space is allowed, we present an O(2kk(n + m)) time algorithm that solves a more general variant with real weights.

Finally, we show that in O(2kpoly(n)) time and space one can count the number of connected vertex covers of size at most k, and this time upper bound can not be improved to O((2 − ε)kpoly(n)) for any ε > 0 under the Strong Exponential Time Hypothesis, as shown by Cygan et al. [CCC’12].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marek Cygan
    • 1
  1. 1.IDSIA, University of LuganoSwitzerland

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